The Art and Obligation of Doubting:

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The Art and Obligation of Doubting Dubitatio in
the 13th Century Jaap Maat, Katherina Rybalko,
Sara L. Uckelman Institute for Logic,
Language, and Computation University of
Amsterdam 1st GPMR Workshop in Logic and
Semantics, 28 June 2007
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What is an obligatio A type of formalized
disputation. Opponent and respondent. Opponent
puts forward statements. Respondent can accept,
reject, or doubt. Roots in Aristotle The
conceptual origins of obligationes can be found
in the dialectical disputations in Aristotle's
Topics. However, there is nothing like dubitatio
in these disputations. Found in medieval logic
from the 13th century.
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Our tract Oxford MS Canon misc 281, ed. by De
Rijk in 1975 as Obligationes Parisienses Tentativ
ely can be placed in early 13th century
France. Early text, but apparently describes
common practice existing for quite some
time. Contains a straightforward presentation of
obligations Has not been thoroughly studied so
far Treats dubitatio relatively extensively
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• purpose of the obligatio
• The aim of disputation is twofold
• knowledge or belief of things simpliciter
• exercise or being exercised
• The 2nd aim is pursued in obligation.
• When there is an obligation about something, one
  argues not only about things true simpliciter,
  but also about the consequences according to the
  obligation. But if the obligatum is true, the
  respondent similarly does not attend to the truth
  or falsity of things except compared to the
  obligation. Whence belief or knowledge of the
  consequences of things is very much acquired by
  this type of disputation.

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Structure of the text Types of
obligatio Classification according to type of
response
obligatio
depositio deny
dubitatio doubt
positio concede
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Structure of the text Types of
obligatio Classification according to type of
initial statement
obligatio
rei veritas
petitio
institutio
certain
uncertain
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• Structure of the text
• types of obligatio
• positio
• - of determinate positio
• - of certain rules for ponible posita
• - six sophisms
• - of indeterminate positio
• - of the twofold mode of indeterminate positio
• dubitatio
• whether dubitatio is an obligation or not
• of certain rules
• a sophism
• depositio
• - of its definition and rules
• - of special depositio

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Dubitatio Whether dubitatio is an obligation or
not Just as someone can be obliged to concede or
deny, so one can be obliged to doubt. Contra a
wise man is not in doubt there is no art in
doubting the response prove it! is that of the
ignorant Solution this is true for absolute
disputation, as discussed in the Topics. But in
restricted or hypothetical disputation, doubting
may be necessary and hence is artful. The author
seems to set obligation apart from dialectical
disputation as treated by Aristotle
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• General rules
• Everything antecedent to the dubitatum must be
  held true or doubtful, that is not false.
• (Omne antecedens ad dubitatum habendum est pro
  vero vel dubio, idest pro non falso)
• Everything following from the dubitatum must be
  held not false, that is true or doubtful.
• (Omne sequens ad dubitatum, habendum est pro non
  falso, idest pro vero vel dubio)

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Comparison with other dubitatio rules Nicholas
of Paris (?) (1230-1250) To every antecedent to
the dubitatum it is to be responded false or
prove it! and never true. Text discussed by
Green (Sherwood ?) For the dubitatum and for
its convertibles and for its contradictory and
for its consequences, if they are false, and for
its antecedents, if they are true, the response
is doubtful. But if the antecedent is false, it
must be denied, and the consequent, if it is
true, must be conceded and the same can be said
of the antecedent and the consequent of things
not convertible. And for irrelevant things the
response is according to its quality.
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• Specific rules (1)
• 3. Certain things antecedent to the dubitatum are
  true, certain are false.
• (Antecedens ad dubitatum quoddam est verum,
  quoddam est falsum)
• Of enuntiables, some are antecedent to the
  dubitatum through themselves (per se), some are
  antecedent to the dubitatum with a conceded
  thing or conceded things or the opposite of a
  denied thing or opposites of denied things.
• (Enuntiabilium quoddam est antecedens per se ad
  dubitatum, quoddam cum concesso vel concessis vel
  opposito negati vel oppositis negati sic vel
  negatorum ad dubitatum)

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• Specific rules (2)
• Everything convertible with the dubitatum and
  every opposite of the dubitatum must be doubted.
• (Omne convertible cum dubitato et omne oppositum
  dubitati est dubitandum)
• 6. Every false antecedent of the dubitatum the
  opposite of which is not a true thing being
  doubted must be denied.
• (Omne falsum antecedens ad dubitatum cuius
  oppositum non est verum dubitatum, est negandum)
• 7. Of things following from the dubitatum, some
  are true, some are false. However every truth
  following from the dubitatum must be conceded,
  but every falsehood following from the dubitatum
  must be doubted.
• (Sequentium ad dubitatum aliud est verum, aliud
  est falsum. Omne autem verum sequens ad
  dubitatum est concedendum, sed omne falsum
  sequens ad dubitatum est dubitandum)

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Specific rules (3) 8. Of things repugnant to
the dubitatum, some are repugnant through
themselves, some through an accident, such as
through a consequence of the dubitatum. (Repugna
ntium dubitato quoddam est repugnans per se,
quoddam per accidens, ut per consequens
dubitati) 9. Of things repugnant to the
dubitatum, some are contradictory opposites or
convertible with them, some are
contraries. (Repugnantium dubitato quoddam est
oppositum contradictorie vel convertibile cum
illo, quoddam contrarium)
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Specific rules (4) 10. Everything repugnant to
the dubitatum through itself and contradictorily
must be doubted, repugnant in truth through
itself and contrary must be held to be not true,
as false, if it is known to be false, and as
doubtful, if it is doubted. Also everything
repugnant per accidens and contradictorily
similarly must be held to be not true, also
similarly for things repugnant per accidens and
contrarily. (Omne repugnans dubitato per se et
contradictorie est dubitandum, repugnans vero per
se at contrarie habendum est pro non vero, ut pro
falso, si sciatur esse falsum, et pro dubio, si
dubitetur. Omne autem repgunans per accidens et
contradictorie similiter habendum est pro non
vero, repugnans autem per accidens et contrarie
similiter)
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• Formalization (1)
• We construct a function ? which when given an
  O-statement returns an A-action.
• First we fix the following
• V a function such that V(p) T if the
  proposition is true in reality and V(p) F
  otherwise.
• d the dubitatum
• We stipulate that hold to be true is equivalent
  to concede, hold to be false' equivalent to
  deny' or negate, and hold to be doubtful
  equivalent to doubt. We then define the
  following notation for A-actions
• C concede
• D doubt
• N negate (or deny)

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• Formalization (2)
• General rules
• 1. ? (d) D (definitional)
• 2. if p ? d, then ? (p) ? N (rule 1)
• 3. if d ? p, then ? (p) ? N (rule 2)

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Formalization (3) Special rules 1. if p ? d,
then V (p) T or V (p) F (rule 3) 2. if d ? p,
then ? (p) D (rule 5) 3. if p ?d, then ? (p)
D (rule 5) 4. if p ? d, if V (p) F, if ? (?p)
? D, then ?(p) N (rule 6) 5. if d ? p and V (p)
T, then ? (p) C (rule 7) 6. if d ? p and V
(p) F, then ? (p) D (rule 7) 7. if p ? d
(read 'p is repugnant to d') then it is one of
these if r ? R1, ? (r) D. If r ? R2, R3,
R4, if V (r) F, ? (r) N and if V (r) ? F, ?
(r) D (rule 10)
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An example dubitatio Assume in rei veritas the
Pope is in Rome, and that it is put forward
Either the Antichrist is black or the pope is in
Rome. O The Antichrist is colored. R Deny
(because it is irrelevant and false). O The
Antichrist is not colored. R Accept (opposite of
something correctly denied). O The Antichrist is
not black. R Accept (follows from something
correctly accepted). O The pope is in Rome. R
Accept (follows from the dubitatum) along with
things correctly accepted or denied, and is
true). Cedat tempus The respondent did badly
because The pope is in Rome implies the
dubitatum, and so should have been doubted.